Millions of users share their opinions on Twitter, making it a valuable platform for tracking and analyzing public sentiment. Such tracking and analysis can provide critical information for decision making in various domains. Therefore it has attracted attention in both academia and industry. Previous research mainly focused on modeling and tracking public sentiment. In this work, we move one step further to interpret sentiment variations. We observed that emerging topics (named foreground topics) within the sentiment variation periods are highly related to the genuine reasons behind the variations. Based on this observation, we propose a Latent Dirichlet Allocation (LDA) based model, Foreground and Background LDA (FB-LDA), to distill foreground topics and filter out longstanding background topics. These foreground topics can give potential interpretations of the sentiment variations. To further enhance the readability of the mined reasons, we select the most representative tweets for foreground topics and develop another generative model called Reason Candidate and Background LDA (RCB-LDA) to rank them with respect to their “popularity” within the variation period. Experimental results show that our methods can effectively find foreground topics and rank reason candidates. The proposed models can also be applied to other tasks such as finding topic differences between two sets of documents.